We introduce a new spectral mixture analysis approach. Unlike most available approaches that only use the spectral information, this approach uses the spectral and spatial information available in the hyperspectral data. Moreover, it does not assume a global convex geometry model that encompasses all the data but rather multiple local convex models. Both the multiple model boundaries and the model's endmembers and abundances are fuzzy. This allows points to belong to multiple groups with different membership degrees. Our approach is based on minimizing a joint objective function to simultaneously learn the underling fuzzy multiple convex geometry models and find a robust estimate of the model's endmembers and abundances.